Minimal Reduction Type and Affine Springer Fibers

2025/04/07 by Anlong Chua, Chua, Anlong
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2504.05113

openalex publication_date 2025/04/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We extend a result of Yun on minimal reduction types to the parahoric case. This implies a uniqueness property for 2-special representations appearing in the cohomology of certain affine Springer fibers. Using this, we settle a conjecture of Lusztig on strata in a reductive group.

Citations

• Lusztig conjectures on S-cells in affine Weyl groups
• Perverse sheaves on infinite-dimensional stacks, and affine Springer theory
• Lusztig's strata are locally closed
• Lectures on Springer theories and orbital integrals
• On conjugacy classes in a reductive group
• The spherical part of the local and global Springer actions
• From conjugacy classes in the Weyl group to unipotent classes, III
• Rigid geometric structures, isometric actions, and algebraic quotients
• Rigid geometric structures, isometric actions, and algebraic quotients
• Unipotent classes and special Weyl group representations
• Affine Demazure modules and T-fixed point subschemes in the affine Grassmannian
• Twisted loop groups and their affine flag varieties
• Induce/restrict matrices for exceptional Weyl groups
• Representations of Coxeter groups and Hecke algebras
• On the Generalized Springer Correspondence for Exceptional Groups

Related

• Witt vector affine Springer fibers
• On the dependence of the affine Springer fibers on their root valuation datum
• On the fundamental domain of affine Springer fibers
• The geometry of some generalized affine Springer fibers
• Dimension des fibres de Springer affines pour les groupes